Time-Dependent Positively Invariant Sets on Cauchy Problems: Applications in Population Dynamics
Abstract
Abstract We establish flow invariance results for semilinear systems governed by non-Hille–Yosida operators under time-dependent closed convex constraints. A new subtangential condition is introduced, together with explicit sufficient conditions for positive invariance formulated in terms of the resolvent and the nonlinear term. The results apply to systems with non-densely defined operators and time-varying constraints, and are illustrated by applications to an age-structured predator–prey model, a biofilm model, and a class of neutral functional differential equations.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Mathematical and Theoretical Epidemiology and Ecology Models
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Acta Applicandae Mathematicae
- Volume
- 201
- Issue
- 1
- Pages
- 15
- Publication date
- 1 February 2026
- Language
- EN